US 2012/0059865 A1Published application

Analysis method using finite element method, and analytical computation program using finite element method

AssigneeAisin Aw Co., Ltd.

InventorsChangcheng SHAO, Toshiya IINUMA

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Abstract

An analysis method using a finite element method includes: selecting an analysis domain to be analyzed; dividing the analysis domain into elements as calculation objects; creating a matrix of each element; integrating a general function term as a product of a Galerkin weight function and a general function; creating simultaneous equations, based on the sum of matrices of respective elements and the sum of values obtained by integrating the general function term, and obtaining a numerical solution from the simultaneous equations. In integrating the general function term, the concept of a nodal domain defined based on a result of discretization of a second-order differential term according to a Galerkin finite element method is introduced, and the general function term using a typical value of the element is integrated.

Claims28

Dependent claims

An analysis method using a finite element method, comprising the steps of:

selecting an analysis domain to be analyzed;
dividing the analysis domain into a plurality of elements as calculation objects;
applying a Galerkin weight function with respect to a given node in a given element as one of the plurality of elements, and performing element integration so as to create a matrix of each of the elements;
integrating a general function term as a product of the Galerkin weight function and a general function;
creating simultaneous equations, based on a sum of matrices of respective elements in a domain around the given node, and a sum of values obtained by integrating the general function term;
introducing a boundary condition into the simultaneous equations;
and
obtaining a numerical solution by solving the simultaneous equations, wherein
in the general function term integrating step, a concept of a nodal domain defined based on a result of discretization of a second-order differential term according to a Galerkin finite element method is introduced, and the general function term using a typical value of the element is integrated.

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An analytical computation program using a finite element method, for causing a computer to perform analytical computations using the finite element method, which causes the computer to execute the steps of:

selecting an analysis domain to be analyzed;
dividing the analysis domain into a plurality of elements as calculation objects;
applying a Galerkin weight function with respect to a given node in a given element as one of the plurality of elements, and performing element integration so as to create a matrix of each of the elements;
integrating a general function term as a product of the Galerkin weight function and a general function, wherein a concept of a nodal domain defined based on a result of discretization of a second-order differential term according to a Galerkin finite element method is introduced, and the general function term using a typical value of the element is integrated;
creating simultaneous equations, based on a sum of matrices of respective elements in a domain around the given node, and a sum of values obtained by integrating the general function term;
introducing a boundary condition into the simultaneous equations;
and
obtaining a numerical solution by solving the simultaneous equations.

5 more elements

Dependencies are inferred from the claim text.